I actually do all those things. I've had interns but I'm the only full time tech guy. The company is 4-6 people right now, depending on how you count. You can call my title exaggerated if you like, but I don't know what else I would call my job.
Also, I'm 24 and I have a master's in CS...I'm not a "manager" in the sense I think you're thinking.
I would call your title exaggerated yet accurate. It's the nature of a small group of people forming a Corporation; you get titles that sound big when they're really not, at least not yet. There's a huge difference between being a CTO of company with hundreds or thousands of employees vs being a CTO of a company with six employees.
Now I've never been a CTO at all, so I'm not trying to disparage you. I hope your company grows and you get the chance to grow into the title. Good luck!
Also, I'm 24 and I have a master's in CS...I'm not a "manager" in the sense I think you're thinking.